WEBVTT
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This is College Physics
Answers with Shaun Dychko.
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We're going to calculate the
centripetal acceleration of the sun
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around the center of
the Milky Way galaxy.
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So the distance from the sun
to the center of the galaxy
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we have to convert from
light-years into meters.
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So a light-year is
the speed of light
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multiplied by a year and I've written
a letter c for the speed of light
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because that's the letter usually
used for speed of light.
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So we can write down speed of
light times a year this way
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in order to make units of meters
because we take the speed of light,
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three times ten to the
eight meters per second
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and then multiply it by a
year written in seconds
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and then we end up with meters.
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So 365 and a quarter days per year
multiplied by 24 hours per day,
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multiplied by 3600
seconds per hour,
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makes these seconds cancel
with these seconds,
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and we're left with
units of meters.
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Then multiply all that by
three times ten to the four,
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we get 2.8402 times ten
to the twenty meters
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is the distance from the sun to the
center of the Milky Way galaxy.
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Then we'll need to find the
angular velocity of the sun.
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So we know it does one complete circle
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which is two pi radians every 2.6
times ten to the eight years
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and we want the units of *omega*
to be in radians per second,
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so we need to convert the years
in the denominator into seconds.
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So multiply by 365 and a
quarter days per year
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and so on and so on,
just as we did up there
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and we end up with 7.658 times ten to
the minus sixteen radians per second.
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Then we take the distance and multiply
by the angular velocity squared
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to get our centripetal
acceleration of 1.67
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times ten to the minus ten
meters per second squared.
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that is such a small number
that it does support the idea
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that the reference frame of the sun
is not accelerating which is --
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what it means to say when you
have an inertial reference frame,
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it means that the reference
frame is not accelerating
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because this number is so small.
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The linear speed of the sun
around the center of the galaxy
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is the distance multiplied
by the angular velocity
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and that works out to 2.18 times
ten to the five meters per second
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which is actually a
very large number
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but nevertheless the centripetal
acceleration is small
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because the distance to
the center is so huge.